In this paper we present our test results with our memetic algorithm, the Discrete Bacterial Memetic Evolutionary Algorithm (DBMEA). The algorithm combines the Bacterial Evolutionary Algorithm with discrete local search techniques (2-opt and 3-opt). The algorithm has been tested on four discrete NP-hard optimization problems so far, on the Traveling Salesman Problem, and on its three variants (the Traveling Salesman Problem with Time Windows, the Traveling Repairman Problem, and the Time Dependent Traveling Salesman Problem). The DBMEA proved to be efficient for all problems: it found optimal or close-optimal solutions. For the Traveling Repairman Problem the DBMEA outperformed even the state-of-the-art methods. The preliminary version of this paper was presented at the 3rd Conference on Information Technology, Systems Research and Computational Physics, 2–5 July 2018, Cracow, Poland [1].